Finite Group Databasebeta

← D11×#2646 #14920214

Subgroups — D11×#2646 #14920214

Order 2816.

2374 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074589C212yesmaximal, complemented
2#13074588C214yesmaximal, complemented
3#13074587C214yesmaximal, complemented
4#13074586C211yesmaximal, characteristic, complemented
5#13074585C214yesmaximal, complemented
6D11×#400C214yesmaximal, complemented
7D11×#398C214yesmaximal, complemented
8D11×#385C214yesmaximal
9D11×#380C212yesmaximal
10C2×D11×#95C211yesmaximal, characteristic
11C11×#2646C211yesmaximal, characteristic, complemented
12C23×C4×D11C2212yes—
13C23×C4×D11C2211yescharacteristic
14C2×C4⋊C4×D11C2212yes—
15C2×C4⋊C4×D11C2212yes—
16C2×C4⋊C4×D11C2214yes—
17C2×C4⋊C4×D11C2214yes—
18C2×C22⋊C4×D11C2214yes—
19C11×#400C2214yescomplemented
20C11×#398C2214yescomplemented
21C11×#385C2214yes—
22C11×#380C2212yes—
23C2×C11×#95C2211yescharacteristic
24#10622825C2212yes—
25#10622823C2214yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2211yescharacteristic
28#10622602C2214yes—
29#10622602C2214yes—
30#10622600C2212yes—
31#10622600C2212yes—
32#10622599C2214yescomplemented
33#10622597C2214yescomplemented
34#10622597C2214yescomplemented
35#10622596C2214yescomplemented
36#10622595C2214yescomplemented
37#10622593C2214yescomplemented
38#10622563C2214yes—
39#10622559C2214yes—
40#10622555C2214yes—
41#10622281C2214yes—
42#10622281C2214yes—
43#10622280C2214yes—
44D11×#95C2214yes—
45D11×#95C2214yes—
46D11×#95C2214yes—
47D11×#95C2214yes—
48D11×#95C2214yes—
49#10622274C2214yescomplemented
50#10622273C2214yescomplemented
51#10622273C2214yescomplemented
52#10622272C2214yescomplemented
53#10622271C2214yescomplemented
54#10622271C2214yescomplemented
55#10622270C2214yescomplemented
56#10622270C2214yescomplemented
57C24×D11C2311yescharacteristic
58C23×C4×C11C2312yes—
59C23×C4×C11C2311yescharacteristic
60C23×Dic11C2312yes—
61C23×Dic11C2311yescharacteristic
62C22×C4×D11—28no—
63C22×C4×D11—44no—
64C22×C4×D11—44no—
65C22×C4×D11—44no—
66C22×C4×D11Q818yes—
67C22×C4×D11C2314yes—
68C22×C4×D11C2314yes—
69C22×C4×D11C2314yes—
70C22×C4×D11C2312yes—
71C22×C4×D11C2314yes—
72C22×C4×D11C2312yes—
73C2×C11×C4⋊C4C2314yes—
74C2×C11×C4⋊C4C2314yes—
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C22⋊C4C2314yes—
78C2×C22⋊Dic11C2314yes—
79C2×(C2×D11)⋊C4C2314yes—
80C2×(C2×D11)⋊C4C2314yes—
81C2×C4⋊Dic11C2312yes—
82C2×C4⋊Dic11C2314yes—
83C2×C4⋊Dic11C2312yes—
84C2×C4⋊Dic11C2314yes—
85C2×Dic11⋊C4C2314yes—
86C2×Dic11⋊C4C2314yes—
87C2×Dic11⋊C4C2314yes—
88C2×Dic11⋊C4C2314yes—
89C2×Dic11⋊C4C2314yes—
90C2×Dic11⋊C4C2314yes—
91C4⋊C4×D11—44no—
92C4⋊C4×D11—44no—
93C4⋊C4×D11—48no—
94C4⋊C4×D11—48no—
95C22⋊C4×D11—216no—
96C11×#95C2314yes—
97C11×#95C2314yes—
98C11×#95C2314yes—
99C11×#95C2314yes—
100C11⋊#95C2314yes—
101C11⋊#95C2314yes—
102C11⋊#95C2314yes—
103C11⋊#95C2314yes—
104C11⋊#95C2314yes—
105C11⋊#95C2314yes—
106C11⋊#95C2314yes—
107C11⋊#95C2314yes—
108C11⋊#95C2314yes—
109C11⋊#95C2314yes—
110C11⋊#95C2314yes—
111C11⋊#95C2314yes—
112C2×#2646—111nomaximal, Sylow
113C24×C11C2411yescharacteristic
114C23×D11—22no—
115C23×D11—24no—
116C23×D11—22no—
117C23×D11C2×Q814yes—
118C23×D11#4118yes—
119C23×D11C2411yescharacteristic
120C23×D11C2411yescharacteristic
121C22×C4×C11—24no—
122C22×C4×C11—42no—
123C22×C4×C11—42no—
124C22×C4×C11—42no—
125C22×C4×C11C2×Q814yes—
126C22×C4×C11C2414yes—
127C22×C4×C11C2414yes—
128C22×C4×C11C2414yes—
129C22×C4×C11C2412yes—
130C22×Dic11—24no—
131C22×Dic11—42no—
132C22×Dic11—42no—
133C22×Dic11—42no—
134C22×Dic11C2×Q814yes—
135C22×Dic11C2414yes—
136C22×Dic11C2414yes—
137C22×Dic11C2414yes—
138C22×Dic11C2412yes—
139C2×C4×D11—28no—
140C2×C4×D11—28no—
141C2×C4×D11—28no—
142C2×C4×D11—28no—
143C2×C4×D11—24no—
144C2×C4×D11—24no—
145C2×C4×D11—28no—
146C2×C4×D11—28no—
147C2×C4×D11—28no—
148C2×C4×D11—28no—
149C2×C4×D11—28no—
150C2×C4×D11—28no—
151C2×C4×D11—42no—
152C2×C4×D11—42no—
153C2×C4×D11—44no—
154C2×C4×D11—44no—
155C2×C4×D11—416no—
156C2×C4×D11—432no—
157C2×C4×D11C2×Q818yes—
158C2×C4×D11C2×Q818yes—
159C11×C4⋊C4—42no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4—44no—
162C11×C4⋊C4—44no—
163C11×C22⋊C4—28no—
164C22⋊Dic11—28no—
165(C2×D11)⋊C4—28no—
166(C2×D11)⋊C4—28no—
167C4⋊Dic11—42no—
168C4⋊Dic11—42no—
169C4⋊Dic11—44no—
170C4⋊Dic11—44no—
171Dic11⋊C4—44no—
172Dic11⋊C4—44no—
173Dic11⋊C4—44no—
174Dic11⋊C4—44no—
175Dic11⋊C4—44no—
176Dic11⋊C4—44no—
177#2646—114no—
178#2646—114no—
179#2646—114no—
180#2646—112no—
181#2646—111no—
182#2646D1111yescharacteristic, direct product factor
183C2×#400—114no—
184C2×#398—114no—
185C2×#385—114no—
186C2×#380—112no—
187C22×#95—111no—
188C23×C11—21no—
189C23×C11—22no—
190C23×C11—21no—
191C23×C11C22×Q812yes—
192C23×C11C2×#4114yes—
193C23×C11C2511yescharacteristic
194C22×D11—21no—
195C22×D11—22no—
196C22×D11—21no—
197C22×D11—216no—
198C22×D11—216no—
199C22×D11—28no—
200C22×D11—28no—
201C22×D11#125116yes—
202C22×D11C22×Q812yes—
203C22×D11C22×Q812yes—
204C22×D11C2×#4114yes—
205C22×D11C2×#4114yes—
206C22×D11H(5,𝔽2)12yes—
207C22×D11H(5,𝔽2)14yes—
208C22×D112−1+412yes—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—44no—
221C2×C4×C11—48no—
222C2×C4×C11C22×Q814yes—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—24no—
226C2×Dic11—24no—
227C2×Dic11—24no—
228C2×Dic11—24no—
229C2×Dic11—24no—
230C2×Dic11—24no—
231C2×Dic11—24no—
232C2×Dic11—24no—
233C2×Dic11—24no—
234C2×Dic11—44no—
235C2×Dic11—48no—
236C2×Dic11C22×Q814yes—
237C4×D11—216no—
238C4×D11—48no—
239C4×D11—416no—
240C4×D11—416no—
241C4×D11—416no—
242C4×D11—416no—
243C24×C4—111no—
244C24×C4—112no—
245C22×C4⋊C4—112no—
246C22×C4⋊C4—114no—
247C22×C4⋊C4—114no—
248C22×C4⋊C4—112no—
249C22×C22⋊C4—114no—
250#400—114no—
251#400—114no—
252#400—114no—
253#400—114no—
254#400—114no—
255#400—114no—
256#400—114no—
257#400C2×D1114yescomplemented
258#398—114no—
259#398—114no—
260#398—114no—
261#398—114no—
262#398—114no—
263#398—114no—
264#398—114no—
265#398C2×D1114yescomplemented
266#385—114no—
267#385—114no—
268#385—114no—
269#385—114no—
270#385—114no—
271#385—114no—
272#385—114no—
273#385C2×D1114yes—
274#380—112no—
275#380—112no—
276#380—112no—
277#380—114no—
278#380—114no—
279#380C2×D1112yes—
280C2×#95—112no—
281C2×#95—111no—
282C2×#95—114no—
283C2×#95—114no—
284C2×#95—114no—
285C2×#95—114no—
286C2×#95—114no—
287C2×#95C2×D1111yescharacteristic
288C22×C11—24no—
289C22×C11—24no—
290C22×C11—22no—
291C22×C11—22no—
292C22×C11C2×#12514yes—
293C22×C11C23×Q811yescharacteristic
294C22×C11C22×#4112yes—
295C22×C11C2×H(5,𝔽2)11yescharacteristic
296C22×C11C2×H(5,𝔽2)12yes—
297C22×C11C2×2−1+411yescharacteristic
298C2×D11—24no—
299C2×D11—24no—
300C2×D11—22no—
301C2×D11—22no—
302C2×D11—232no—
303C2×D11C2×#12514yes—
304C2×D11C2×#12514yes—
305C2×D11#53818yes—
306C2×D11#53918yes—
307C2×D11#54314yes—
308C2×D11#54414yes—
309C4×C11—24no—
310C4×C11—44no—
311C4×C11—44no—
312C4×C11—44no—
313Dic11—24no—
314Dic11—44no—
315Dic11—44no—
316Dic11—44no—
317C25—111no—
318C23×C4—111no—
319C23×C4—112no—
320C23×C4—118no—
321C23×C4—112no—
322C23×C4—112no—
323C23×C4—114no—
324C23×C4—114no—
325C23×C4—114no—
326C23×C4—114no—
327C23×C4—228no—
328C23×C4—444no—
329C23×C4—444no—
330C23×C4—444no—
331C23×C4C22×D1112yes—
332C23×C4C22×D1111yescharacteristic
333C2×C4⋊C4—114no—
334C2×C4⋊C4—112no—
335C2×C4⋊C4—114no—
336C2×C4⋊C4—112no—
337C2×C4⋊C4—114no—
338C2×C4⋊C4—114no—
339C2×C4⋊C4—114no—
340C2×C4⋊C4—114no—
341C2×C4⋊C4—114no—
342C2×C4⋊C4—114no—
343C2×C4⋊C4—444no—
344C2×C4⋊C4—444no—
345C2×C4⋊C4—448no—
346C2×C4⋊C4—448no—
347C2×C4⋊C4C22×D1112yes—
348C2×C4⋊C4C22×D1112yes—
349C2×C4⋊C4C22×D1114yes—
350C2×C4⋊C4C22×D1114yes—
351C2×C22⋊C4—114no—
352C2×C22⋊C4—114no—
353C2×C22⋊C4—114no—
354C2×C22⋊C4—2216no—
355C2×C22⋊C4C22×D1114yes—
356#95—114no—
357#95—114no—
358#95—114no—
359#95—114no—
360#95—114no—
361#95—114no—
362#95—114no—
363#95—114no—
364#95—114no—
365#95—114no—
366#95—114no—
367#95—114no—
368#95C22×D1114yes—
369#95C22×D1114yes—
370#95C22×D1114yes—
371#95C22×D1114yes—
372C2×C11—24no—
373C2×C11C22×#12511yescharacteristic
374C2×C11C2×#53812yes—
375C2×C11C2×#53912yes—
376C2×C11C2×#54311yescharacteristic
377C2×C11C2×#54411yescharacteristic
378D11—24no—
379D11#264618yesdirect product factor
380C24—111no—
381C24—114no—
382C24—118no—
383C24—111no—
384C24—222no—
385C24—224no—
386C24—222no—
387C24C23×D1111yescharacteristic
388C22×C4—24no—
389C22×C4—42no—
390C22×C4—42no—
391C22×C4—42no—
392C22×C4—112no—
393C22×C4—114no—
394C22×C4—118no—
395C22×C4—118no—
396C22×C4—114no—
397C22×C4—114no—
398C22×C4—114no—
399C22×C4—224no—
400C22×C4—224no—
401C22×C4—228no—
402C22×C4—228no—
403C22×C4—228no—
404C22×C4—228no—
405C22×C4—228no—
406C22×C4—228no—
407C22×C4—228no—
408C22×C4—228no—
409C22×C4—228no—
410C22×C4—228no—
411C22×C4—224no—
412C22×C4—442no—
413C22×C4—442no—
414C22×C4—444no—
415C22×C4—444no—
416C22×C4—4416no—
417C22×C4—4432no—
418C22×C4—442no—
419C22×C4—442no—
420C22×C4—442no—
421C22×C4Q8×D1114yes—
422C22×C4C23×D1114yes—
423C22×C4C23×D1114yes—
424C22×C4C23×D1114yes—
425C22×C4C23×D1112yes—
426C4⋊C4—42no—
427C4⋊C4—42no—
428C4⋊C4—44no—
429C4⋊C4—44no—
430C4⋊C4—444no—
431C4⋊C4—444no—
432C4⋊C4—444no—
433C4⋊C4—444no—
434C4⋊C4—444no—
435C4⋊C4—444no—
436C4⋊C4—442no—
437C4⋊C4—442no—
438C4⋊C4—444no—
439C4⋊C4—444no—
440C22⋊C4—28no—
441C22⋊C4—228no—
442C22⋊C4—228no—
443C22⋊C4—228no—
444C11C2×#264611yescharacteristic, complemented, Sylow
445C23—21no—
446C23—22no—
447C23—21no—
448C23—112no—
449C23—114no—
450C23—112no—
451C23—114no—
452C23—112no—
453C23—112no—
454C23—114no—
455C23—1116no—
456C23—2216no—
457C23—228no—
458C23—2216no—
459C23—228no—
460C23—221no—
461C23—222no—
462C23—221no—
463C23C2×Q8×D1112yes—
464C23#41×D1114yes—
465C23C24×D1111yescharacteristic
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—44no—
478C2×C4—48no—
479C2×C4—114no—
480C2×C4—2216no—
481C2×C4—222no—
482C2×C4—222no—
483C2×C4—224no—
484C2×C4—224no—
485C2×C4—224no—
486C2×C4—224no—
487C2×C4—224no—
488C2×C4—224no—
489C2×C4—224no—
490C2×C4—224no—
491C2×C4—224no—
492C2×C4—448no—
493C2×C4—4416no—
494C2×C4—4416no—
495C2×C4—4416no—
496C2×C4—4416no—
497C2×C4—444no—
498C2×C4—448no—
499C2×C4C2×Q8×D1114yes—
500C22—24no—
501C22—24no—
502C22—22no—
503C22—22no—
504C22—114no—
505C22—118no—
506C22—118no—
507C22—114no—
508C22—114no—
509C22—114no—
510C22—2232no—
511C22—224no—
512C22—224no—
513C22—222no—
514C22—222no—
515C22D11×#12514yes—
516C22C22×Q8×D1111yescharacteristic
517C22C2×#41×D1112yes—
518C22D11×H(5,𝔽2)11yescharacteristic
519C22D11×H(5,𝔽2)12yes—
520C22D11×2−1+411yescharacteristic
521C4—24no—
522C4—44no—
523C4—44no—
524C4—44no—
525C4—224no—
526C4—444no—
527C4—444no—
528C4—444no—
529C2—24no—
530C2—118no—
531C2—224no—
532C2C2×D11×#12511yescharacteristic
533C2D11×#53812yes—
534C2D11×#53912yes—
535C2D11×#54311yescharacteristic
536C2D11×#54411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2646C2
prime radicalC24×D11C23
hypercenter#2646D11
hypocenterC11C2×#2646
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2646

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13074589C2semidirect
2. #13074588C2semidirect
3. #13074587C2semidirect
4. #13074586C2semidirect
5. #13074585C2semidirect
6. D11×#400C2semidirect
7. D11×#398C2semidirect
11. C11×#2646C2semidirect
19. C11×#400C22semidirect
20. C11×#398C22semidirect
32. #10622599C22semidirect
33. #10622597C22semidirect
34. #10622597C22semidirect
35. #10622596C22semidirect
36. #10622595C22semidirect
37. #10622593C22semidirect
49. #10622274C22semidirect
50. #10622273C22semidirect
51. #10622273C22semidirect
52. #10622272C22semidirect
53. #10622271C22semidirect
54. #10622271C22semidirect
55. #10622270C22semidirect
56. #10622270C22semidirect
182. #2646D11direct (N × H)
257. #400C2×D11semidirect
265. #398C2×D11semidirect
379. D11#2646direct (N × H)
444. C11C2×#2646semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130745892
#130745882
#130745872
#130745862
#130745852
D11×#4002
D11×#3982
D11×#3852
D11×#3802
C2×D11×#952
C11×#26462
C2×#264611